Log-Sobolev Inequality for the Continuum Sine-Gordon Model


Type
Article
Change log
Authors
Bauerschmidt, Roland  ORCID logo  https://orcid.org/0000-0001-7453-2737
Bodineau, T 
Abstract

We derive a multiscale generalisation of the Bakry--'Emery criterion for a measure to satisfy a Log-Sobolev inequality. Our criterion relies on the control of an associated PDE well known in renormalisation theory: the Polchinski equation. It implies the usual Bakry--'Emery criterion, but we show that it remains effective for measures which are far from log-concave. Indeed, using our criterion, we prove that the massive continuum Sine-Gordon model with β<6π satisfies asymptotically optimal Log-Sobolev inequalities for Glauber and Kawasaki dynamics. These dynamics can be seen as singular SPDEs recently constructed via regularity structures, but our results are independent of this theory.

Description
Keywords
math.PR, math.PR, math-ph, math.AP, math.MP
Journal Title
Communications on Pure and Applied Mathematics
Conference Name
Journal ISSN
0010-3640
1097-0312
Volume Title
74
Publisher
Wiley
Rights
All rights reserved
Sponsorship
EPSRC Grant Number EP/R014604/1 ANR-15-CE40-0020-01 grant LSD